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Existence of weak solutions to a Cahn–Hilliard–Biot system
Abels, Helmut
, Garcke, Harald
und Haselböck, Jonas
(2024)
Existence of weak solutions to a Cahn–Hilliard–Biot system.
Nonlinear Analysis: Real World Applications 81, S. 104194.
Veröffentlichungsdatum dieses Volltextes: 29 Aug 2024 06:47
Artikel
DOI zum Zitieren dieses Dokuments: 10.5283/epub.59014
Zusammenfassung
We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot’s equations for poroelasticity, including phase-field dependent material properties, with the Cahn–Hilliard equation to model the evolution of the solid, and is further augmented by a visco-elastic ...
We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot’s equations for poroelasticity, including phase-field dependent material properties, with the Cahn–Hilliard equation to model the evolution of the solid, and is further augmented by a visco-elastic regularization of Kelvin–Voigt type. To obtain this result, we approximate the problem in two steps, where first a semi-Galerkin ansatz is employed to show existence of weak solutions to regularized systems, for which later on compactness arguments allow limit passage. Notably, we also establish a maximal regularity theory for linear visco-elastic problems.
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| Dokumentenart | Artikel | ||||
| Titel eines Journals oder einer Zeitschrift | Nonlinear Analysis: Real World Applications | ||||
| Verlag: | Elsevier | ||||
|---|---|---|---|---|---|
| Band: | 81 | ||||
| Seitenbereich: | S. 104194 | ||||
| Datum | 22 August 2024 | ||||
| Institutionen | Mathematik > Prof. Dr. Helmut Abels Mathematik > Prof. Dr. Harald Garcke | ||||
| Identifikationsnummer |
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| Klassifikation |
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| Stichwörter / Keywords | Cahn–Hilliard equation, Biot’s equations, Poroelasticity, Existence analysis, Mixed boundary conditions, Maximal regularity | ||||
| Dewey-Dezimal-Klassifikation | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
| Status | Veröffentlicht | ||||
| Begutachtet | Ja, diese Version wurde begutachtet | ||||
| An der Universität Regensburg entstanden | Ja | ||||
| URN der UB Regensburg | urn:nbn:de:bvb:355-epub-590148 | ||||
| Dokumenten-ID | 59014 |
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